Name: active filter design and frequency response
Uploaded: 2025-05-22T09:06:15.000Z
Duration: 1 min 25 s
Channel: JoVE

Certain passive filters incorporate expensive inductors designed not to exceed unity gain. These filters may exhibit reduced attenuation efficacy at frequencies below the audio range.
Active filters consist of operational amplifiers, resistors, and capacitors.
Employed in audio processing, telecommunications, and power supply units, these filters are categorized as first-order low-pass, first-order high-pass, band-pass, and band-reject filters.
Consider the transfer functions and frequency responses of low-pass and high-pass active filters.
Unlike passive filters, the finite low-frequency gain in low-pass active filters and the high-frequency gain in high-pass active filters depend on the feedback-to-input resistor ratio.
Low-pass filters attenuate frequencies above the corner frequency, while high-pass filters suppress those below the corner frequency.
The combination of low-pass and high-pass filters results in a band-pass filter, while a band-reject filter combines both types with a summing amplifier.
Band-pass filters transmit frequencies between the corner frequencies and reject those outside; band-reject filters block frequencies within the range and allow external frequencies.

active filters

Active filters are electronic circuits that use operational amplifiers (op-amps), resistors, and capacitors to filter out unwanted frequency components from a signal. A first-order low-pass active filter is designed to pass signals with a frequency lower than a certain cutoff frequency and attenuate frequencies higher than that cutoff frequency. The transfer function for a first-order low-pass active filter is:
<img alt="Transfer function equation H(s)=Af/(1+s/&#969;c); control systems; stability analysis." src="/files/ftp_upload/15149/15149_Equation_1.svg" style="text-align: center; height: 40px;" data-altupdatedat="1754904545000" data-alt="Transfer function equation: H(s)=Af/(1+s/wc), mathematical formula for control system analysis." />
 Where Af is the gain at low frequencies also known as the dc gain, s is the complex frequency, and &#969;c is the corner or cutoff frequency. A first-order high-pass active filter allows signals above a certain cutoff frequency to pass while attenuating signals below this frequency. Its transfer function can be expressed as:
<img alt="Transfer function equation H(s)=Afs/(s+&#969;c); symbolic representation in control systems." src="/files/ftp_upload/15149/15149_Equation_2.svg" style="text-align: center; height: 36px;" data-altupdatedat="1754904545000" data-alt="Transfer function formula H(s) = (Afs)/(s+&#969;c), control systems, signal processing equation." />
Where Af represents the gain at high frequencies, and &#969;c is the cutoff frequency below which the output is significantly reduced. A band-pass filter has combined properties of low-pass and high-pass filters. It permits only a certain range of frequencies to pass through while attenuating frequencies outside this range. The transfer function of a band-pass filter has the form:
<img alt="Transfer function equation H(s) for filter design; includes parameters s, Af, &#969;c, and Q." src="/files/ftp_upload/15149/15149_Equation_3.svg" style="text-align: center; height: 42px;" data-altupdatedat="1754904545000" data-alt="Transfer function equation H(s) for filter design analysis; frequency response optimization." />
Here &#969;0 is the center frequency, and Q is the quality factor. A band-reject filter, also known as a notch filter, does the opposite by allowing most frequencies to pass, except for a specific range that it attenuates. The standard transfer function for a band-reject filter is:
<img alt="Transfer function equation H(s) for electronic filter analysis, formula, control systems." src="/files/ftp_upload/15149/15149_Equation_4.svg" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Transfer function equation H(s) for RLC circuit; includes parameters Q and &#969; for signal analysis." />
In active filters, the gain within the passband can be set independently of the cutoff frequency, the gain is determined by the ratio of the feedback resistor to the input resistor, and the design parameters, such as resistor and capacitor values are chosen to set the cutoff frequencies and to shape the overall frequency response of the filter to meet specific requirements.

Active Filters

Active filters are electronic circuits that use operational amplifiers (op-amps), resistors, and capacitors to filter out unwanted frequency components ...

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JoVE Core

Electrical Engineering

Unit 1

Frequency Response

KEY TERMS AND CONCEPTS

active filter design and frequency response

Active filters use op-amps, resistors, and capacitors to shape a signal's frequency response. They remove unwanted frequency components while keeping the parts of the signal that are needed. The design depends on the choice of resistor and capacitor values, which set the cutoff points and help define the overall response.

A first-order low-pass active filter passes signals below a cutoff frequency and reduces signals above it. Its transfer function includes the low-frequency gain, also called the dc gain, along with the complex frequency s and the corner or cutoff frequency ωc. A first-order high-pass active filter does the opposite. It lets signals above a cutoff frequency pass and reduces signals below that frequency.

Active filters can also be built as band-pass filters. These filters combine low-pass and high-pass behavior and allow only a certain range of frequencies to pass. Their transfer function includes the center frequency ω0 and the quality factor Q. A band-reject filter, also called a notch filter, works in the opposite way. It passes most frequencies but attenuates a specific range.

In active filters, the gain in the passband can be set independently of the cutoff frequency. The gain is determined by the ratio of the feedback resistor to the input resistor. By choosing resistor and capacitor values carefully, engineers can set the cutoff frequencies and shape the frequency response to meet specific needs.

Active Filter Design and Frequency Response

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Learn how active filters use op-amps, resistors, and capacitors to shape frequency response with low-pass, high-pass, band-pass, and notch designs.

Active Filter Design and Frequency Response | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Active Filter Design and Frequency Response

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